Stir together yeast, brown sugar, and 1/4 cup warm water in a large bowl until yeast is dissolved. Let stand until foamy, about 15 minutes. (If mixture doesn't foam, discard and start over with new yeast.).
Whisk together rye flour, 1 cup all-purpose flour, zest, salt, anise seeds, cumin, and 1/2 teaspoon caraway seeds. Add flour mixture along with melted butter, molasses, and remaining 3/4 cup warm water to yeast mixture and beat with an electric mixer at medium speed 5 minutes. Reduce speed to low and add 1/2 cup all-purpose flour, beating until combined. Add remaining 1/4 cup plus 1 tablespoon all-purpose flour and beat until incorporated. (Dough will be very sticky.) Scrape down dough from side of bowl with a rubber spatula and let rise, bowl covered tightly with plastic wrap, in a draft-free place at warm room temperature until doubled in bulk, about 1 1/2 hours.
Put oven rack in middle position and preheat oven to 350°F Butter muffin pans.
Stir down dough (it will be too sticky to punch down). Divide dough evenly among 24 muffin cups, about a rounded tablespoon per cup. (Grease tablespoon with oil as necessary to prevent sticking.) Let dough rest, uncovered, in a draft-free place at warm room temperature 30 minutes. Gently brush tops of muffins with some of egg wash, then sprinkle with sea salt and remaining 1/4 teaspoon caraway seeds.
Bake until muffins are puffed and a wooden pick or skewer inserted into center comes out clean, 25 to 35 minutes. Turn out muffins onto a rack and cool to warm or room temperature.